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September 23, 2023

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Description

Nonlinear Vibration. Instructor: Prof. S. K. Dwivedy, Department of Mechanical Engineering, IIT Guwahati.

This course is meant for the senior undergraduate and postgraduate students of Mechanical Engineering, Civil Engineering and Aerospace Engineering. The course provides a brief introduction to linear and nonlinear vibration, and then it discusses the development of nonlinear governing equation of motion, analytical solution methods, stability and bifurcation analysis, numerical techniques, and applications of nonlinear vibrations. (from nptel.ac.in)

Course Curriculum

    • Lecture 01 – Introduction to Nonlinear Systems Unlimited
    • Lecture 02 – Review of Linear Vibrating Systems Unlimited
    • Lecture 03 – Phenomena associated with Nonlinear Systems Unlimited
    • Lecture 04 – Commonly Observed Phenomena in Nonlinear Systems Unlimited
    • Lecture 05 – Force and Moment based Approach Unlimited
    • Lecture 06 – Hamilton’s Principle and Lagrange Principle Unlimited
    • Lecture 07 – Derivation of Equation of Motion of Nonlinear Discrete System Unlimited
    • Lecture 08 – Derivation of Equation of Motion of Nonlinear Continuous System Unlimited
    • Lecture 09 – Derivation of Equation of Motion of Nonlinear Continuous System (cont.) Unlimited
    • Lecture 10 – Ordering Techniques in the Nonlinear Equations Unlimited
    • Lecture 11 – Qualitative Analysis – Straight Forward Expansions Unlimited
    • Lecture 12 – Numerical Method – Straight Forward Expansions Unlimited
    • Lecture 13 – Lindstedt-Poincare Method Unlimited
    • Lecture 14 – Method of Multiple Scales Unlimited
    • Lecture 15 – Method of Harmonic Balance Unlimited
    • Lecture 16 – Method of Averaging Unlimited
    • Lecture 17 – Generalized Method of Averaging Unlimited
    • Lecture 18 – Krylov-Bogoliubov-Mitropolsky Method of Averaging Unlimited
    • Lecture 19 – Incremental Harmonic Balance Method, Intrinsic Multiple Harmonic Balance Method Unlimited
    • Lecture 20 – Modified Lindstedt Poincare Method Unlimited
    • Lecture 21 – Stability and Bifurcation of Fixed Point Response 1 Unlimited
    • Lecture 21 – Stability and Bifurcation of Fixed Point Response 1 Unlimited
    • Lecture 22 – Stability and Bifurcation of Fixed Point Response 2 Unlimited
    • Lecture 23 – Stability and Bifurcation of Fixed Point Response 3 Unlimited
    • Lecture 24 – Stability and Bifurcation of Fixed Point Response 4 Unlimited
    • Lecture 25 – Stability and Bifurcation Analysis of Periodic Responses Unlimited
    • Lecture 26 – Bifurcation of Periodic Responses, Introduction to Quasi-Periodic and … Unlimited
    • Lecture 27 – Quasi-Periodic and Chaotic Responses Unlimited
    • Lecture 28 – Numerical Methods to Obtain Roots of Characteristic Equation and Time Response Unlimited
    • Lecture 29 – Numerical Methods to Obtain Time Response Unlimited
    • Lecture 30 – Numerical Methods to Obtain Frequency Response Unlimited
    • Lecture 31 – Free Vibration of Single Degree of Freedom Nonlinear Systems With Cubic and … Unlimited
    • Lecture 32 – Free Vibration of Single Degree of Freedom Nonlinear Systems With Cubic and … Unlimited
    • Lecture 33 – Free Vibration of Multi-Degree of Freedom Nonlinear Systems With Cubic and … Unlimited
    • Lecture 34 – Forced Vibration of Single Degree of Freedom Nonlinear Systems With Cubic … Unlimited
    • Lecture 35 – Nonlinear Forced-Vibration of Single and Multi Degree-of-Freedom System Unlimited
    • Lecture 36 – Nonlinear Forced-Vibration of Single and Multi Degree-of-Freedom System (cont.) Unlimited
    • Lecture 37 – Nonlinear Forced-Vibration of Multi-Degree-of-Freedom System Unlimited
    • Lecture 38 – Nonlinear Vibration of Parametrically Excited System: Axially Loaded Sandwich Beam Unlimited
    • Lecture 39 – Nonlinear Vibration of Parametrically Excited System Unlimited
    • Lecture 40 – Nonlinear Vibration of Parametrically Excited System with Internal Resonances Unlimited

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